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Date: Tue, 29 Nov 2011 03:57:40 +0000 (UTC)
From: =?utf-8?Q?S=C3=A9bastien_Brisard_=28Created=29_=28JIRA=29?=
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Subject: [jira] [Created] (MATH-715) PascalDistribution returns wrong values
 of mean and variance
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PascalDistribution returns wrong values of mean and variance
------------------------------------------------------------

                 Key: MATH-715
                 URL: https://issues.apache.org/jira/browse/MATH-715
             Project: Commons Math
          Issue Type: Bug
            Reporter: S=C3=A9bastien Brisard


The header of the Javadoc states that the random variable (say X) being rep=
resented by this {{o.a.c.m.distribution.PascalDistribution}} is the number =
of *failures*. The current Javadoc is slightly confusing, because it refers=
 to the Wikipedia website, where the opposite convention is adopted (X is t=
he number of *successes*) : different formulas therefore apply for the mean=
 and variance of X. The javadoc should be made clearer, for example by incl=
usion of full formulas. Also the parameters differing from the Wikipedia re=
ference should not have the same name
  * {{p}} is the probability of success in both cases: OK,
  * {{r}} is the number of failures in Wikipedia, but the number of success=
es in CM. This could be renamed (say) {{s}}.

Finally, with the current notations of CM, the mean of X is given by {{mean=
(X) =3D r * (1 - p) / p}}, while the currently implemented formula is {{r *=
 p / (1 - p)}}, which is actually the formula corresponding to the Wikipedi=
a convention.

The following piece of code shows that the current implementation is faulty
{code:java}
public class PascalDistributionDemo {
   public static void main(String[] args) {
       final int r =3D 10;
       final double p =3D 0.2;
       final int numTerms =3D 1000;
       final PascalDistribution distribution =3D new PascalDistribution(r, =
p);
       double mean =3D 0.;
       for (int k =3D numTerms - 1; k >=3D 0; k--) {
           mean +=3D k * distribution.probability(k);
       }
       // The following prints 40.00000000000012
       System.out.println("Estimate of the mean =3D " + mean);
       // The following prints 2.5
       System.out.println("CM implementation =3D " +
                          distribution.getNumericalMean());
       // The following prints 2.5
       System.out.println("r * p / (1 - p) =3D " + (r * p / (1 - p)));
       // The following prints 40.0
       System.out.println("r * (1 - p) / p =3D " + (r * (1 - p) / p));
   }
}
{code}


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